Spline Knots and Their Control Polygons With Differing Knottedness

Carlo H. Séquin

Spline knots based on Bézier curves or B-splines can exhibit a knot type that is different from that exhibited by its control polygon, i.e., the spline and its control polygon are not ambient isotopic. By forming composite knots from suitably designed building blocks the difference in knottedness of the two 1-manifolds can be made arbitrarily large.

BibTeX citation:

@techreport{Séquin:EECS-2009-152,
Author = {Séquin, Carlo H.},
Title = {Spline Knots and Their Control Polygons With Differing Knottedness},
Institution = {EECS Department, University of California, Berkeley},
Year = {2009},
Month = {Nov},
URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-152.html},
Number = {UCB/EECS-2009-152},
Abstract = {Spline knots based on Bézier curves or B-splines can exhibit a knot type that is different from that exhibited by its control polygon, i.e., the spline and its control polygon are not ambient isotopic. By forming composite knots from suitably designed building blocks the difference in knottedness of the two 1-manifolds can be made arbitrarily large.}
}